Simplify the following expression: $ p = \dfrac{-9q + 2}{10q - 5} - \dfrac{10}{7} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-9q + 2}{10q - 5} \times \dfrac{7}{7} = \dfrac{-63q + 14}{70q - 35} $ Multiply the second expression by $\dfrac{10q - 5}{10q - 5}$ $ \dfrac{10}{7} \times \dfrac{10q - 5}{10q - 5} = \dfrac{100q - 50}{70q - 35} $ Therefore $ p = \dfrac{-63q + 14}{70q - 35} - \dfrac{100q - 50}{70q - 35} $ Now the expressions have the same denominator we can simply subtract the numerators: $p = \dfrac{-63q + 14 - (100q - 50) }{70q - 35} $ Distribute the negative sign: $p = \dfrac{-63q + 14 - 100q + 50}{70q - 35}$ $p = \dfrac{-163q + 64}{70q - 35}$